How to Calculate R^2 in Tensorflow

Question

I am trying to do regression in Tensorflow. I'm not positive I am calculating R^2 correctly as Tensorflow gives me a different answer than sklearn.metrics.r2_score Can someone please look at my below code and let me know if I implemented the pictured equation correctly. Thanks

total_error = tf.square(tf.sub(y, tf.reduce_mean(y)))
unexplained_error = tf.square(tf.sub(y, prediction))
R_squared = tf.reduce_mean(tf.sub(tf.div(unexplained_error, total_error), 1.0))
R = tf.mul(tf.sign(R_squared),tf.sqrt(tf.abs(R_squared)))

Answer 1

What you are computing the "R^2" is

compared to the given expression, you are computing the mean at the wrong place. You should take the mean when computing the errors, before doing the division.

unexplained_error = tf.reduce_sum(tf.square(tf.sub(y, prediction)))
total_error = tf.reduce_sum(tf.square(tf.sub(y, tf.reduce_mean(y))))
R_squared = tf.sub(1, tf.div(unexplained_error, total_error))

Answer 2

The function is given here:

def R_squared(y, y_pred):
  residual = tf.reduce_sum(tf.square(tf.subtract(y, y_pred)))
  total = tf.reduce_sum(tf.square(tf.subtract(y, tf.reduce_mean(y))))
  r2 = tf.subtract(1.0, tf.div(residual, total))
  return r2

The concept is explained here.

Answer 3

I would strongly recommend against using a recipe to calculate this! The examples I've found do not produce consistent results, especially with just one target variable. This gave me enormous headaches!

The correct thing to do is to use tensorflow_addons.metrics.RQsquare(). Tensorflow Add Ons is on PyPi here and the documentation is a part of Tensorflow here. All you have to do is set y_shape to the shape of your output, often it is (1,) for a single output variable.